Implications

We have the following indirect implication of form equivalence classes:

387 \(\Rightarrow\) 0
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
387 \(\Rightarrow\) 0

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
387:

DPO:  Every infinite set has a non-trivial, dense partial order.  (A partial ordering \(<\) on a set \(X\) is dense if \((\forall x, y\in X)(x \lt y \to (\exists z \in X)(x \lt z \lt y))\) and is non-trivial if \((\exists x,y\in X)(x \lt y)\)).

0:  \(0 = 0\).

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